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blagie [28]
3 years ago
5

Given that f(x)= 2x+1 and g(x)= x^2 +2x+1 find (F+g)(2). Find (F.g)(x) find f(x)/g find f(2) +g(-2)?

Mathematics
2 answers:
Pepsi [2]3 years ago
7 0

Answer:

(f+g)(2) = 14

f(g(x)) = 2x^2 + 4x +3

\frac{f(x)}{g(x)} = \frac{2x+1}{x^2+2x+1}

f(2) + g(-2) = 6

Step-by-step explanation:

Function composition and transformation combines functions together using operations such as addition, subtraction, multiplication, division and substitution. To find each, perform the operation with the functions f(x) = 2x+1 and g(x) = x^2 + 2x +1.

(f+g)(x) is the functions f and g added together with 2 substituted for x.

(f+g)(x) = 2x+1 + x^2 +2x + 1 = x^2 + 4x + 2\\(f+g)(2) = 2^2 + 4(2) + 2 = 14

(f·g)(x) is function composition that means f(g(x)) or substitute g(x) into f(x).

f(g(x)) = 2(x^2+2x+1)+1 = 2x^2 + 4x+2 + 1\\f(g(x)) = 2x^2 + 4x +3

f(x) / g(x) is division of the two functions. Division can only occur with polynomials if they share the same factors or things which multiply to create them. If none are present, do not simplify.

\frac{f(x)}{g(x)} = \frac{2x+1}{x^2+2x+1}

This cannot be simplified.

f(2) + g(-2) means find the function value of f at 2 and the function value of g at -2 then add them together.

f(2)+g(-2) = 2(2)+1 + ((-2)^2+2(-2) + 1)\\f(2) + g(-2) = 5 + (4-4+1)\\f(2) + g(-2) = 5 +1 = 6

schepotkina [342]3 years ago
4 0

Answer:

Answer:

Step-by-step explanation:

Function composition and transformation combines functions together using operations such as addition, subtraction, multiplication, division and substitution. To find each, perform the operation with the functions f(x) = 2x+1 and .

(f+g)(x) is the functions f and g added together with 2 substituted for x.

(f·g)(x) is function composition that means f(g(x)) or substitute g(x) into f(x).

f(x) / g(x) is division of the two functions. Division can only occur with polynomials if they share the same factors or things which multiply to create them. If none are present, do not simplify.

This cannot be simplified.

f(2) + g(-2) means find the function value of f at 2 and the function value of g at -2 then add them together.

Step-by-step explanation:

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frutty [35]

Answer:

3(2x^2-3x+14)

Step-by-step explanation:

6x^2-9x+42

All three terms have a common factor of 3

3(2x^2-3x+14)

Now let's focus on 2x^2-3x+14 and bring down the factor 3 later

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Let's try to find two factors for ac that multiply to be a*c and add up to be b.

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Even if I made these pairs with both negatives nothing would give me -3

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